# The Rise and Fall of Network Stars: Analyzing 2.5 million graphs to reveal how high-degree vertices emerge over time

## TL;DR

This study analyzes the evolution of 2.5 million graphs from 38,000 real-world networks to understand how high-degree vertices, or network stars, emerge and decline over time, revealing key factors influencing network topology.

## Contribution

It provides the first large-scale analysis of network evolution and introduces a new generative model that explains the rise and fall of network stars based on real-world data.

## Key findings

- Vertices connecting at similar times tend to link more frequently.
- The rate of new vertex addition significantly influences network structure.
- Fast-growing networks are more likely to develop prominent high-degree vertices.

## Abstract

Trends change rapidly in today's world, prompting this key question: What is the mechanism behind the emergence of new trends? By representing real-world dynamic systems as complex networks, the emergence of new trends can be symbolized by vertices that "shine." That is, at a specific time interval in a network's life, certain vertices become increasingly connected to other vertices. This process creates new high-degree vertices, i.e., network stars. Thus, to study trends, we must look at how networks evolve over time and determine how the stars behave. In our research, we constructed the largest publicly available network evolution dataset to date, which contains 38,000 real-world networks and 2.5 million graphs. Then, we performed the first precise wide-scale analysis of the evolution of networks with various scales. Three primary observations resulted: (a) links are most prevalent among vertices that join a network at a similar time; (b) the rate that new vertices join a network is a central factor in molding a network's topology; and (c) the emergence of network stars (high-degree vertices) is correlated with fast-growing networks. We applied our learnings to develop a flexible network-generation model based on large-scale, real-world data. This model gives a better understanding of how stars rise and fall within networks, and is applicable to dynamic systems both in nature and society.